Would I be crazy?

So my husband and I have a 7 year old and a 12 week old. Both boys. There is a local animal rescue that travels to nearby states and rescues animals from abuse and neglect. One of my friends fosters rescued dogs for them. She told me they rescued and brought back 4 dogs in September. The one she is fostering is a chocolate lab and had she was pregnant... she had her puppies last month. The mom and other 3 dogs already have their forever families (yay 🥰) but they are still looking for homes for the puppies. My husband and I have talked about getting a puppy for a long time, even before our youngest was born, but we wanted to adopt and rescue puppies go so fast.

Now... would I be crazy to get one of these puppies when we have a 12 week old? Part of me thinks it would be good timing because I’m up at night with the baby so I’d be up already to take the dog out for night time bathroom trips. And our son obviously isn’t mobile yet so we could have the puppy trained before he starts crawling and just block it out of the room when he’s on the floor until it’s trained. Plus I’m home pretty much all the time so the puppy can be watched and not be in a kennel. The other part of me thinks it’s an insane idea, but I know it would make a great Christmas gift for our oldest. Has anyone tackled a puppy and a baby at the same time? Is this just a horrible idea?